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GR9677 #67 |
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Alternate Solutions |
scottopoly
2006-11-03 19:55:34 | I once heard that if the Earth were compressed into a black hole, it would be about the size of a grape. I think that is a much faster solution. ;) |  | ben
2006-11-03 15:21:30 | i've generally seen the schwarzchild radius derived from the escape velocity as shown in
http://scienceworld.wolfram.com/physics/SchwarzschildRadius.html | |
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Comments |
ivalmian
2008-03-25 19:42:17 | Um, well, the reason it's called the Schwarzschild radius is that it comes from Schwarzschild's solution of Einstein's equations. Take a look:
http://en.wikipedia.org/wiki/Deriving_the_Schwarzschild_solution |  | bat_pesso
2007-10-31 13:50:31 | i don't think relativity is such an issue here, the escape velocity depends only on the mass of the earth, not on the mass of the particle.
thus 0.5c^2 is still GM/R | | Jeremy
2007-10-18 13:17:00 | Not having seen such hardcore hand waving before, I would not feel comfortable with this solution even if I had thought of it. Looking in my books afterwards, I found something that's pretty cool: you can get  from dimensional analysis! (Of course you have to pick the right parameters.) And check this out,  , so unless the proportionality factor is several orders of magnitude, the closest answer is (C).
Moral: If thou needeth formulae, consulteth dimensional analysis. I think I gave up on this problem too quickly, when I could have at least submitted an educated guess. | | chri5tina
2006-11-28 05:24:22 | So in all this handwaving, did he explain the 1/2?
chri5tina
2006-11-28 05:32:11 |
well, I answered my own stupid question, however I'm hitting a bug when I try to edit my above post. I get this error when I try to edit:
omg are you trying to edit someone else's comment, you phisher?! (if you're innocent, then you ought to remember to login.)
when I am already logged in. and I'm not sure where to submit bugs.
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|  | scottopoly
2006-11-03 19:55:34 | I once heard that if the Earth were compressed into a black hole, it would be about the size of a grape. I think that is a much faster solution. ;) | | ben
2006-11-03 15:21:30 | i've generally seen the schwarzchild radius derived from the escape velocity as shown in
http://scienceworld.wolfram.com/physics/SchwarzschildRadius.html | | pablojm
2006-10-28 15:30:36 | This is a good argument to convince someone who doesn't know physics, but how do you know it works...?
evanb
2008-07-01 17:22:24 |
Unfortunately, the way would know it works is by doing the general relativity. You can deduce that in the Schwarzschild metric for a point mass, any timelike or null (lightlike) trajectory (ie. any trajectory that a particle might take) that starts within R = 2M will ever wind up outside of R = 2M ( G = c = 1).
Un-unfortunately, GR reproduces lots of "Newtonian" results. You can even do most cosmology with Newtonian math. Why does that work? Because someone did it fully-general-relativistically and found that the math wound up the same...
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